A high-order compact finite-difference lattice Boltzmann method for simulation of natural convection

In the present work, compact finite-difference lattice Boltzmann method (CFDLBM) is extended to simulate natural convection in square and concentric-circular-annulus cavities, in two-dimensions, for Rayleigh numbers in the range of 10 3 to 10 9 . Owing to the finite-difference discretization of the method, non-uniform and curvilinear grids with a finer near-wall grid resolution could be used in the present simulations. The use of high-order methods further enabled the simulations to be run on relatively coarse meshes when compared with simulations that used classical lattice Boltzmann method. The simulation results are analyzed with the help of streamlines, isothermal contours and temperature, velocity, Nusselt number variations along the walls. The average Nusselt number on the hot wall shows less than 1% error for natural convection in the square cavity study. The circular-annular-cavity is found to have laminar flow for Rayleigh numbers in the range of 10 3 –10 6 and it becomes unsteady and chaotic from 10 7 onwards. The instantaneous and time-average contours of isotherms and streamlines were used to study the unsteady behavior of the flow. A universal near-wall velocity profile is found to exist in all the unsteady natural convection studies in the annular cavity case. The location of the maximum velocities occurring in the annulus is analyzed for all the Rayleigh numbers. The spectra of velocity magnitude fluctuations and temperature fluctuations indicate that the unsteadiness in the cavity is dominant around 0.001 Hz. Natural convection in sine-walled and concentric star shaped cavities are simulated to demonstrate the ability of the present solver to handle complex geometries. The present results indicate that CFDLBM can be successfully used to simulate steady and unsteady chaotic natural convection flows in both rectangular and curvilinear geometries accurately.